Method Of Lines Pde Analysis In Biomedical Science And Engineering

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Method of Lines PDE Analysis in Biomedical Science and Engineering

William E. Schiesser
Method of Lines PDE Analysis in Biomedical Science and Engineering Book PDF

Author : William E. Schiesser
Publisher : John Wiley & Sons
Page : 372 pages
File Size : 43,9 Mb
Release : 2016-04-18
Category : Mathematics
ISBN : 9781119130482

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Method of Lines PDE Analysis in Biomedical Science and Engineering by William E. Schiesser Pdf

Presents the methodology and applications of ODE and PDE models within biomedical science and engineering With an emphasis on the method of lines (MOL) for partial differential equation (PDE) numerical integration, Method of Lines PDE Analysis in Biomedical Science and Engineering demonstrates the use of numerical methods for the computer solution of PDEs as applied to biomedical science and engineering (BMSE). Written by a well-known researcher in the field, the book provides an introduction to basic numerical methods for initial/boundary value PDEs before moving on to specific BMSE applications of PDEs. Featuring a straightforward approach, the book’s chapters follow a consistent and comprehensive format. First, each chapter begins by presenting the model as an ordinary differential equation (ODE)/PDE system, including the initial and boundary conditions. Next, the programming of the model equations is introduced through a series of R routines that primarily implement MOL for PDEs. Subsequently, the resulting numerical and graphical solution is discussed and interpreted with respect to the model equations. Finally, each chapter concludes with a review of the numerical algorithm performance, general observations and results, and possible extensions of the model. Method of Lines PDE Analysis in Biomedical Science and Engineering also includes: Examples of MOL analysis of PDEs, including BMSE applications in wave front resolution in chromatography, VEGF angiogenesis, thermographic tumor location, blood-tissue transport, two fluid and membrane mass transfer, artificial liver support system, cross diffusion epidemiology, oncolytic virotherapy, tumor cell density in glioblastomas, and variable grids Discussions on the use of R software, which facilitates immediate solutions to differential equation problems without having to first learn the basic concepts of numerical analysis for PDEs and the programming of PDE algorithms A companion website that provides source code for the R routines Method of Lines PDE Analysis in Biomedical Science and Engineering is an introductory reference for researchers, scientists, clinicians, medical researchers, mathematicians, statisticians, chemical engineers, epidemiologists, and pharmacokineticists as well as anyone interested in clinical applications and the interpretation of experimental data with differential equation models. The book is also an ideal textbook for graduate-level courses in applied mathematics, BMSE, biology, biophysics, biochemistry, medicine, and engineering.

Time Delay ODE/PDE Models

W.E. Schiesser
Time Delay ODE PDE Models Book PDF

Author : W.E. Schiesser
Publisher : CRC Press
Page : 251 pages
File Size : 42,5 Mb
Release : 2019-11-25
Category : Mathematics
ISBN : 9781000763614

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Time Delay ODE/PDE Models by W.E. Schiesser Pdf

Time delayed (lagged) variables are an inherent feature of biological/physiological systems. For example, infection from a disease may at first be asymptomatic, and only after a delay is the infection apparent so that treatment can begin.Thus, to adequately describe physiological systems, time delays are frequently required and must be included in the equations of mathematical models. The intent of this book is to present a methodology for the formulation and computer implementation of mathematical models based on time delay ordinary differential equations (DODEs) and partial differential equations (DPDEs). The DODE/DPDE methodology is presented through a series of example applications, particularly in biomedical science and engineering (BMSE). The computer-based implementation of the example models is explained with routines coded (programmed) in R, a quality, open-source scientific computing system that is readily available from the Internet. Formal mathematics is minimized, e.g., no theorems and proofs. Rather, the presentation is through detailed examples that the reader/researcher/analyst can execute on modest computers. The DPDE analysis is based on the method of lines (MOL), an established general algorithm for PDEs, implemented with finite differences. The example applications can first be executed to confirm the reported solutions, then extended by variation of the parameters and the equation terms, and even the forumulation and use of alternative DODE/DPDE models. • Introduces time delay ordinary and partial differential equations (DODE/DPDEs) and their numerical computer-based integration (solution) • Illustrates the computer implementation of DODE/DPDE models with coding (programming) in R, a quality, open-source scientific programming system readily available from the Internet • Applies DODE/DPDE models to biological/physiological systems through a series of examples • Provides the R routines for all of the illustrative applications through a download link • Facilitates the use of the models with reasonable time and effort on modest computers

Differential Equation Analysis in Biomedical Science and Engineering

William E. Schiesser
Differential Equation Analysis in Biomedical Science and Engineering Book PDF

Author : William E. Schiesser
Publisher : John Wiley & Sons
Page : 280 pages
File Size : 45,8 Mb
Release : 2014-03-31
Category : Mathematics
ISBN : 9781118705162

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Differential Equation Analysis in Biomedical Science and Engineering by William E. Schiesser Pdf

Features a solid foundation of mathematical and computational tools to formulate and solve real-world PDE problems across various fields With a step-by-step approach to solving partial differential equations (PDEs), Differential Equation Analysis in Biomedical Science and Engineering: Partial Differential Equation Applications with R successfully applies computational techniques for solving real-world PDE problems that are found in a variety of fields, including chemistry, physics, biology, and physiology. The book provides readers with the necessary knowledge to reproduce and extend the computed numerical solutions and is a valuable resource for dealing with a broad class of linear and nonlinear partial differential equations. The author’s primary focus is on models expressed as systems of PDEs, which generally result from including spatial effects so that the PDE dependent variables are functions of both space and time, unlike ordinary differential equation (ODE) systems that pertain to time only. As such, the book emphasizes details of the numerical algorithms and how the solutions were computed. Featuring computer-based mathematical models for solving real-world problems in the biological and biomedical sciences and engineering, the book also includes: R routines to facilitate the immediate use of computation for solving differential equation problems without having to first learn the basic concepts of numerical analysis and programming for PDEs Models as systems of PDEs and associated initial and boundary conditions with explanations of the associated chemistry, physics, biology, and physiology Numerical solutions of the presented model equations with a discussion of the important features of the solutions Aspects of general PDE computation through various biomedical science and engineering applications Differential Equation Analysis in Biomedical Science and Engineering: Partial Differential Equation Applications with R is an excellent reference for researchers, scientists, clinicians, medical researchers, engineers, statisticians, epidemiologists, and pharmacokineticists who are interested in both clinical applications and interpretation of experimental data with mathematical models in order to efficiently solve the associated differential equations. The book is also useful as a textbook for graduate-level courses in mathematics, biomedical science and engineering, biology, biophysics, biochemistry, medicine, and engineering.

Time Delay ODE/PDE Models

W.E. Schiesser
Time Delay ODE PDE Models Book PDF

Author : W.E. Schiesser
Publisher : CRC Press
Page : 235 pages
File Size : 52,5 Mb
Release : 2019-11-25
Category : Medical
ISBN : 9781000763737

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Time Delay ODE/PDE Models by W.E. Schiesser Pdf

Time delayed (lagged) variables are an inherent feature of biological/physiological systems. For example, infection from a disease may at first be asymptomatic, and only after a delay is the infection apparent so that treatment can begin. Thus, to adequately describe physiological systems, time delays are frequently required and must be included in the equations of mathematical models. The intent of this book is to present a methodology for the formulation and computer implementation of mathematical models based on time delay ordinary differential equations (DODEs) and partial differential equations (DPDEs). The DODE/DPDE methodology is presented through a series of example applications, particularly in biomedical science and engineering (BMSE). The computer-based implementation of the example models is explained with routines coded (programmed) in R, a quality, open-source scientific computing system that is readily available from the Internet. Formal mathematics is minimized, for example, no theorems and proofs. Rather, the presentation is through detailed examples that the reader/researcher/analyst can execute on modest computers. The DPDE analysis is based on the method of lines (MOL), an established general algorithm for PDEs, implemented with finite differences. The example applications can first be executed to confirm the reported solutions, then extended by variation of the parameters and the equation terms, and even the formulation and use of alternative DODE/DPDE models.

ODE/PDE Analysis of Multiple Myeloma

William E. Schiesser
ODE PDE Analysis of Multiple Myeloma Book PDF

Author : William E. Schiesser
Publisher : CRC Press
Page : 127 pages
File Size : 48,6 Mb
Release : 2020-05-28
Category : Mathematics
ISBN : 9781000057270

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ODE/PDE Analysis of Multiple Myeloma by William E. Schiesser Pdf

Multiple myeloma is a form of bone cancer. Specifically, it is a cancer of the plasma cells found in bone marrow (bone soft tissue). Normal plasma cells are an important part of the immune system. Mathematical models for multiple myeloma based on ordinary and partial differential equations (ODE/PDEs) are presented in this book, starting with a basic ODE model in Chapter 1, and concluding with a detailed ODE/PDE model in Chapter 4 that gives the spatiotemporal distribution of four dependent variable components in the bone marrow and peripheral blood: (1) protein produced by multiple myeloma cells, termed the M protein, (2) cytotoxic T lymphocytes (CTLs), (3) natural killer (NK) cells, and (4) regulatory T cells (Tregs). The computer-based implementation of the example models is presented through routines coded (programmed) in R, a quality, open-source scientific computing system that is readily available from the Internet. Formal mathematics is minimized, e.g., no theorems and proofs. Rather, the presentation is through detailed examples that the reader/researcher/analyst can execute on modest computers using the R routines that are available through a download. The PDE analysis is based on the method of lines (MOL), an established general algorithm for PDEs, implemented with finite differences.

Partial Differential Equation Analysis in Biomedical Engineering

W. E. Schiesser
Partial Differential Equation Analysis in Biomedical Engineering Book PDF

Author : W. E. Schiesser
Publisher : Cambridge University Press
Page : 433 pages
File Size : 53,7 Mb
Release : 2013
Category : Mathematics
ISBN : 9781107022805

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Partial Differential Equation Analysis in Biomedical Engineering by W. E. Schiesser Pdf

Gives graduate students and researchers an introductory overview of partial differential equation analysis of biomedical engineering systems through detailed examples.

Numerical Modeling of COVID-19 Neurological Effects

William Schiesser
Numerical Modeling of COVID 19 Neurological Effects Book PDF

Author : William Schiesser
Publisher : CRC Press
Page : 196 pages
File Size : 50,6 Mb
Release : 2021-12-26
Category : Mathematics
ISBN : 9781000509953

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Numerical Modeling of COVID-19 Neurological Effects by William Schiesser Pdf

Covid-19 is primarily a respiratory disease which results in impaired oxygenation of blood. The O2-deficient blood then moves through the body, and for the study in this book, the focus is on the blood flowing to the brain. The dynamics of blood flow along the brain capillaries and tissue is modeled as systems of ordinary and partial differential equations (ODE/PDEs). The ODE/PDE methodology is presented through a series of examples, 1. A basic one PDE model for O2 concentration in the brain capillary blood. 2. A two PDE model for O2 concentration in the brain capillary blood and in the brain tissue, with O2 transport across the blood brain barrier (BBB). 3. The two model extended to three PDEs to include the brain functional neuron cell density. Cognitive impairment could result from reduced neuron cell density in time and space (in the brain) that follows from lowered O2 concentration (hypoxia). The computer-based implementation of the example models is presented through routines coded (programmed) in R, a quality, open-source scientific computing system that is readily available from the Internet. Formal mathematics is minimized, e.g., no theorems and proofs. Rather, the presentation is through detailed examples that the reader/researcher/analyst can execute on modest computers. The PDE analysis is based on the method of lines (MOL), an established general algorithm for PDEs, implemented with finite differences. The routines are available from a download link so that the example models can be executed without having to first study numerical methods and computer coding. The routines can then be applied to variations and extensions of the blood/brain hypoxia models, such as changes in the ODE/PDE parameters (constants) and form of the model equations.

Spatiotemporal Modeling of Influenza

William E. Schiesser
Spatiotemporal Modeling of Influenza Book PDF

Author : William E. Schiesser
Publisher : Springer Nature
Page : 97 pages
File Size : 42,5 Mb
Release : 2022-05-31
Category : Technology & Engineering
ISBN : 9783031016653

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Spatiotemporal Modeling of Influenza by William E. Schiesser Pdf

This book has a two-fold purpose: (1) An introduction to the computer-based modeling of influenza, a continuing major worldwide communicable disease. (2) The use of (1) as an illustration of a methodology for the computer-based modeling of communicable diseases. For the purposes of (1) and (2), a basic influenza model is formulated as a system of partial differential equations (PDEs) that define the spatiotemporal evolution of four populations: susceptibles, untreated and treated infecteds, and recovereds. The requirements of a well-posed PDE model are considered, including the initial and boundary conditions. The terms of the PDEs are explained. The computer implementation of the model is illustrated with a detailed line-by-line explanation of a system of routines in R (a quality, open-source scientific computing system that is readily available from the Internet). The R routines demonstrate the straightforward numerical solution of a system of nonlinear PDEs by the method of lines (MOL), an established general algorithm for PDEs. The presentation of the PDE modeling methodology is introductory with a minumum of formal mathematics (no theorems and proofs), and with emphasis on example applications. The intent of the book is to assist in the initial understanding and use of PDE mathematical modeling of communicable diseases, and the explanation and interpretation of the computed model solutions, as illustrated with the influenza model.

Nonlinear Higher Order Differential And Integral Coupled Systems: Impulsive And Integral Equations On Bounded And Unbounded Domains

Feliz Manuel Minhos,Robert De Sousa
Nonlinear Higher Order Differential And Integral Coupled Systems Impulsive And Integral Equations On Bounded And Unbounded Domains Book PDF

Author : Feliz Manuel Minhos,Robert De Sousa
Publisher : World Scientific
Page : 243 pages
File Size : 46,6 Mb
Release : 2022-04-11
Category : Mathematics
ISBN : 9789811225147

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Nonlinear Higher Order Differential And Integral Coupled Systems: Impulsive And Integral Equations On Bounded And Unbounded Domains by Feliz Manuel Minhos,Robert De Sousa Pdf

Boundary value problems on bounded or unbounded intervals, involving two or more coupled systems of nonlinear differential and integral equations with full nonlinearities, are scarce in the literature. The present work by the authors desires to fill this gap. The systems covered here include differential and integral equations of Hammerstein-type with boundary constraints, on bounded or unbounded intervals. These are presented in several forms and conditions (three points, mixed, with functional dependence, homoclinic and heteroclinic, amongst others). This would be the first time that differential and integral coupled systems are studied systematically. The existence, and in some cases, the localization of the solutions are carried out in Banach space, following several types of arguments and approaches such as Schauder's fixed-point theorem or Guo-Krasnosel'ski? fixed-point theorem in cones, allied to Green's function or its estimates, lower and upper solutions, convenient truncatures, the Nagumo condition presented in different forms, the concept of equiconvergence, Carathéodory functions, and sequences. Moreover, the final part in the volume features some techniques on how to relate differential coupled systems to integral ones, which require less regularity. Parallel to the theoretical explanation of this work, there is a range of practical examples and applications involving real phenomena, focusing on physics, mechanics, biology, forestry, and dynamical systems, which researchers and students will find useful.

A Compendium of Partial Differential Equation Models

William E. Schiesser,Graham W. Griffiths
A Compendium of Partial Differential Equation Models Book PDF

Author : William E. Schiesser,Graham W. Griffiths
Publisher : Cambridge University Press
Page : 491 pages
File Size : 42,8 Mb
Release : 2009-03-16
Category : Computers
ISBN : 9780521519861

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A Compendium of Partial Differential Equation Models by William E. Schiesser,Graham W. Griffiths Pdf

Presents numerical methods and computer code in Matlab for the solution of ODEs and PDEs with detailed line-by-line discussion.

Introduction to Numerical Methods for Variational Problems

Hans Petter Langtangen,Kent-Andre Mardal
Introduction to Numerical Methods for Variational Problems Book PDF

Author : Hans Petter Langtangen,Kent-Andre Mardal
Publisher : Springer Nature
Page : 395 pages
File Size : 40,6 Mb
Release : 2019-09-26
Category : Mathematics
ISBN : 9783030237882

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Introduction to Numerical Methods for Variational Problems by Hans Petter Langtangen,Kent-Andre Mardal Pdf

This textbook teaches finite element methods from a computational point of view. It focuses on how to develop flexible computer programs with Python, a programming language in which a combination of symbolic and numerical tools is used to achieve an explicit and practical derivation of finite element algorithms. The finite element library FEniCS is used throughout the book, but the content is provided in sufficient detail to ensure that students with less mathematical background or mixed programming-language experience will equally benefit. All program examples are available on the Internet.

Spline Collocation Methods for Partial Differential Equations

William E. Schiesser
Spline Collocation Methods for Partial Differential Equations Book PDF

Author : William E. Schiesser
Publisher : John Wiley & Sons
Page : 566 pages
File Size : 42,9 Mb
Release : 2017-05-22
Category : Mathematics
ISBN : 9781119301035

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Spline Collocation Methods for Partial Differential Equations by William E. Schiesser Pdf

A comprehensive approach to numerical partial differential equations Spline Collocation Methods for Partial Differential Equations combines the collocation analysis of partial differential equations (PDEs) with the method of lines (MOL) in order to simplify the solution process. Using a series of example applications, the author delineates the main features of the approach in detail, including an established mathematical framework. The book also clearly demonstrates that spline collocation can offer a comprehensive method for numerical integration of PDEs when it is used with the MOL in which spatial (boundary value) derivatives are approximated with splines, including the boundary conditions. R, an open-source scientific programming system, is used throughout for programming the PDEs and numerical algorithms, and each section of code is clearly explained. As a result, readers gain a complete picture of the model and its computer implementation without having to fill in the details of the numerical analysis, algorithms, or programming. The presentation is not heavily mathematical, and in place of theorems and proofs, detailed example applications are provided. Appropriate for scientists, engineers, and applied mathematicians, Spline Collocation Methods for Partial Differential Equations: Introduces numerical methods by first presenting basic examples followed by more complicated applications Employs R to illustrate accurate and efficient solutions of the PDE models Presents spline collocation as a comprehensive approach to the numerical integration of PDEs and an effective alternative to other, well established methods Discusses how to reproduce and extend the presented numerical solutions Identifies the use of selected algorithms, such as the solution of nonlinear equations and banded or sparse matrix processing Features a companion website that provides the related R routines Spline Collocation Methods for Partial Differential Equations is a valuable reference and/or self-study guide for academics, researchers, and practitioners in applied mathematics and engineering, as well as for advanced undergraduates and graduate-level students.

PDE Modeling of Tissue Engineering and Regenerative Medicine

William E. Schiesser
PDE Modeling of Tissue Engineering and Regenerative Medicine Book PDF

Author : William E. Schiesser
Publisher : Elsevier
Page : 190 pages
File Size : 47,6 Mb
Release : 2022-08-20
Category : Computers
ISBN : 9780443187414

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PDE Modeling of Tissue Engineering and Regenerative Medicine by William E. Schiesser Pdf

PDE Modeling of Tissue Engineering and Regenerative Medicine: Computer Analysis in R presents the formulation and computer implementation of mathematical models for the forefront research areas of tissue engineering and regenerative medicine. The mathematical model discussed in this book consists of a system of eight partial differential equations (PDEs) with dependent variables. The computer-based example models are presented through routines coded in R—a quality, open-source scientific computing system that is readily available from the Internet. Formal mathematics is minimized, e.g., no theorems and proofs. Includes detailed examples that the reader can execute on modest computers. Includes PDE routines based on the method of lines (MOL) for computer-based implementation of PDE models Offers transportable computer source codes for readers in R, with line-by-line code descriptions as it relates to the mathematical model and algorithms Authored by a leading researcher and educator in PDE models

Finite Difference Computing with PDEs

Hans Petter Langtangen,Svein Linge
Finite Difference Computing with PDEs Book PDF

Author : Hans Petter Langtangen,Svein Linge
Publisher : Springer
Page : 522 pages
File Size : 49,8 Mb
Release : 2017-06-21
Category : Computers
ISBN : 9783319554563

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Finite Difference Computing with PDEs by Hans Petter Langtangen,Svein Linge Pdf

This book is open access under a CC BY 4.0 license. This easy-to-read book introduces the basics of solving partial differential equations by means of finite difference methods. Unlike many of the traditional academic works on the topic, this book was written for practitioners. Accordingly, it especially addresses: the construction of finite difference schemes, formulation and implementation of algorithms, verification of implementations, analyses of physical behavior as implied by the numerical solutions, and how to apply the methods and software to solve problems in the fields of physics and biology.

Certified Reduced Basis Methods for Parametrized Partial Differential Equations

Jan S Hesthaven,Gianluigi Rozza,Benjamin Stamm
Certified Reduced Basis Methods for Parametrized Partial Differential Equations Book PDF

Author : Jan S Hesthaven,Gianluigi Rozza,Benjamin Stamm
Publisher : Springer
Page : 131 pages
File Size : 45,5 Mb
Release : 2015-08-20
Category : Mathematics
ISBN : 9783319224701

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Certified Reduced Basis Methods for Parametrized Partial Differential Equations by Jan S Hesthaven,Gianluigi Rozza,Benjamin Stamm Pdf

This book provides a thorough introduction to the mathematical and algorithmic aspects of certified reduced basis methods for parametrized partial differential equations. Central aspects ranging from model construction, error estimation and computational efficiency to empirical interpolation methods are discussed in detail for coercive problems. More advanced aspects associated with time-dependent problems, non-compliant and non-coercive problems and applications with geometric variation are also discussed as examples.